1. Field of the Invention
The present invention relates to an integration circuit and, more particularly, to an integration circuit having a variable time constant, which is applied to an active filter and the like.
2. Description of the Related Art
Recently, active filters have been formed into high-frequency ICs. Attempts have been made to integrate an active filter having a video frequency (several MHz) used for video devices such as a VTR and a TV receiver into an IC together with a capacitor. If the frequency of an active filter is further increased, it is expected that a high-precision low-pass filter having a frequency of 20 MHz to 35 MHz used for a high quality television, and a high-Q band-pass filter which is operated at a frequency of several tens MHz and used in the field of communication can be realized.
If an active filter having a frequency band above several MHz is realized by an operational amplifier type filter constituted by two amplifying stages, good frequency characteristics are difficult to obtain due to a need for phase compensation. For this reason, when an active filter having a high frequency band is to be realized, an integration circuit constituted by a differential amplifier having a capacitor as a load is used. An integration circuit constituting an active filter must satisfy the following requirements:
a. it has a variable time constant so as to allow correction of variations in capacitance value of a capacitor integrated in an IC;
b. it has a high S/N ratio when an active filter is formed; and
c. it has a small distortion factor.
The performance required for the integration circuit to satisfy the requirement b will be described below.
The S/N ratio of the filter is defined as the ratio of the input level range (Vr) of the differential amplifier constituting the integration circuit to a square root .sqroot.(Vout.sup.2) of the square average of output noise voltage outputs from the filter, as indicated by equation (1): ##EQU1##
According to the analysis result described in reference 1: "High frequency CMOS continous-time filters", the output noise voltage .sqroot./(Vout.sup.2) is proportional to the square average of equivalent input noise voltages Vin, the filter Q, and a center frequency fo and is given by equation (2) below for a quadratic filter: ##EQU2## where .DELTA.f is the bandwidth.
According to equations (1) and (2), it is apparent that the S/N ratio of an active filter can be increased by using an integration circuit having a large ratio of the input level range Vr to the equivalent input noise voltage Vin.
An integration circuit constituted by a gain cell is widely used as a conventional integration circuit for an active filter. For example, this integration circuit is used for a multipurpose filter disclosed in reference: Published Unexamined Japanese Patent Application No. 58-161413. When the product of a transconductance gm of a transistor Q3 and an emitter degeneration resistance R.sub.E is sufficiently larger than 1 (gm.multidot.R.sub.E &gt;&gt;1) due to the local feedback by the emitter degeneration resistance R.sub.E, the nonlinearity of a differential amplifier constituted by transistors Q1 and Q2 is improved to have linear I/O characteristics. Furthermore, an input level range as large as gm.multidot.R.sub.E times that of a circuit without the emitter degeneration resistance R.sub.E (100 mVpp.times.gm RE) can be obtained.
A transconductance Gm of the gain cell is the product of the reciprocal of the emitter degeneration resistance R.sub.E and the ratio of a current I1 to a current I2, i.e., (1/R.sub.E)(I.sub.1 /I.sub.2). An integration circuit used for an active filter is required to have a variable time constant to change the characteristics (mainly, a cutoff frequency or a center frequency) of the filter.
In the conventional integration circuit, an output from the differential amplifier is logarithmically compressed by a transistor Q5 and is subsequently expanded by the transistor Q3 to extract an output signal Vout. In addition, the total transconductance can be changed by changing the value of the current I.sub.2 or I.sub.1, thus changing the time constant. In this integration circuit, therefore, noise is amplified in the process of compression/expansion, and the square average Vint2 of the equivalent input noise voltages is given by equation (3) below, assuming that I.sub.1 =I.sub.2, and that integration circuit is driven by a circuit having a low output impedance for the sake of simple explanation. In this case, shot noise generated by the base current is too small to be considered. ##EQU3## for n=gm.multidot.R.sub.E, where k is a Boltzmann's constant, T is the absolute temperature, R.sub.B is the base resistance of a transistor, and Gm is the transconductance of a gain cell. For the sake of comparison, an equivalent input noise voltage Vint'.sup.2 of the most basic differential amplifier without the emitter degeneration resistance R.sub.E is given by equation (4): ##EQU4## where gm' is the transconductance of a transistor.
In this case, assuming that the two types of transconductances Gm and gm' are equal in value, it is found from the comparison between equations (3) and (4) that thermal noise due to the base resistance R.sub.B and the shot noise are increased .sqroot.2.multidot.n times and .sqroot.(2n+2) times, respectively, in terms of voltage value. Since the noise is increased with the expansion of the input level range, an increase in S/N ratio cannot be expected much.
According to an integration circuit disclosed in reference: "Gyrator Video Filter IC with Automatic Tuning", IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL SC-15, DECEMBER, 1980, pp. 965, FIG. 7, 1980, only the linearity is improved by the emitter degeneration resistance R.sub.E, and noise is not amplified because logarithmic compression/expansion is not performed as in the gain cell in the conventional filter. The square average Vint.sup.2 of the equivalent input noise voltages of this circuit is given by the following equation, provided that the transconductance of the latter conventional circuit is represented by Gm': ##EQU5## The noise output from the circuit is very small as compared with the gain cell, and the noise is not increased with the expansion of the input level range (n.fwdarw.large).
In the latter conventional integration circuit, even if, for example, the value of the current I.sub.1 is changed, the transconductance Gm' does not change. For this reason, as shown in FIG. 7, the time constant of the integration circuit must be controlled by using a varactor diode as a load capacitance and changing a bias voltage V.sub.B to change the capacitance. With this arrangement, however, since the load capacitance is changed by an input signal, distortion is inevitably caused. In addition, since the capacitance variable range of a varactor diode is generally difficult to widen, the variable range of the time constant of the integration circuit is narrow. If, therefore, an active filter is constituted by this integration circuit, variations in cutoff frequency cannot often be corrected to obtain a desired frequency. If the capacitance variable range of the varactor diode is widened, the distortion based on variations in load capacitance of an input signal is increased.
As described above, in the integration circuit constituted by the conventional gain cell, the time constant can be easily changed over a wide range by changing the transconductance of the differential amplifier, but noise is amplified. In the integration circuit whose time constant is changed by the varactor diode, the variable range of time constants is narrow, and distortion is increased with the expansion of the variable range.